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Some kinds of -fuzzy filters of -algebras

✍ Scribed by Xueling Ma; Jianming Zhan; Wiesław A. Dudek

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
632 KB
Volume
58
Category
Article
ISSN
0898-1221

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✦ Synopsis

∈, ∈ ∨q)-fuzzy (implicative, positive implicative, fantastic) filter (∈, ∈ ∨ q)-fuzzy (implicative, positive implicative, fantastic) filter Fuzzy (implicative, positive implicative, fantastic) filter with thresholds a b s t r a c t

The concepts of (∈, ∈ ∨ q)-fuzzy (implicative, positive implicative and fantastic) filters of BL-algebras are introduced and some related properties are investigated. Some characterizations of these generalized fuzzy filters are derived. In particular, we describe the relationships among ordinary fuzzy (implicative, positive implicative and fantastic) filters, (∈, ∈ ∨ q)-fuzzy (implicative, positive implicative and fantastic) filters and (∈, ∈ ∨ q)-fuzzy (implicative, positive implicative and fantastic) filters of BL-algebras. Finally, we prove that a fuzzy set F of a BL-algebra L is an (∈, ∈ ∨ q)-fuzzy implicative filter of L if and only if it is both an (∈, ∈ ∨ q)-fuzzy positive implicative filter and an (∈, ∈ ∨ q)-fuzzy fantastic filter.

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